The refund is a lie
A common advice related to RRSP is "you must absolutely reinvest your refund". Some people even go a step further and say "if you don't, you're missing out on the whole point of the RRSP". Some people insist even more strongly on being wrong and will say things along the lines of "if you don't reinvest your tax refund, you're going to get taxed twice on the same money".
It is a common misconception, but the truth is that the refund should be irrelevant in your decision to contribute in your RRSP in any given tax year. If you want to compare the total returns of TFSA vs RRSP for example, the refund plays absolutely no role.
The only thing that matters in making a proper comparison is grossing up your after-tax contribution to make sure you're comparing the same things. Reinvesting the refund is one way to gross-up your contribution, but it is far from the only one.
Now let's be clear: it is true that you end up with more money in your pocket down the road when you reinvest your refund, but that's only because when you invest more money, you end up with more money invested. I know, shocker!
Simple illustration
Imagine a scenario where you have a 40% marginal tax rate, $10k available in chequing that you would like to invest in your RRSP, and you also have a $3000 bill coming up. What's the best move?
#1: You've been told you must absolutely reinvest your tax refund, therefore you contribute $7,000 now, keep $3,000 aside to pay the bill, and reinvest your $2,800 refund when you get it.
#2: You understand that money is fungible so you contribute the entire $10,000 now. When you get the $4,000 refund, you use it for the bill and reinvest the $1000 left.
In scenario #1, you end up with an RRSP balance of $9,800. In scenario #2, you end up with an RRSP balance of $11,000. In both cases the $3000 bill has been paid and there's $0 left in chequing. How is this possible? Simple: you invested more after-tax money in scenario 2 than in scenario 1. Of course if you invest more you get a bigger balance!
Even better yet, consider scenario #3:
#3: You pay the $3000 bill right now, and invest the remaining $7000. You borrow $4666.66 and invest that too, to get your total RRSP contributions to $11,666.66. 40% of that is $4,666.66 which is enough to pay back the loan (with some minimal interest paid)
Suddenly you now have $11,666.66 in your RRSP at the same point in time as in #1 and #2, the bill has also been paid and you also have $0 left in chequing. How is that possible? Simple: you invested more after-tax money than in other scenarios. Of course if you invest more you get a bigger balance!
The deception actually lies in the fact that the reinvested refund in #1 and #2 takes place in a different tax year, so you'll get a refund on that contribution, but you have to wait a full year for it. By doing a "gross-up loan" like in scenario #3, you essentially get the immediate result of reinvesting your refund recursively for infinitely many years (or until you get to less than a penny refunded or run out of RRSP room).
Granted, not everybody has access to cheap credit or a well-funded up emergency fund to temporarily dip into in order to do this magic gross-up trick. What's being shown here is everything that goes inside the RRSP immediately becomes pre-tax, and will become post-tax once you withdraw. There especially is no such thing as getting taxed twice on the same money if you misuse the refund.
Refund or not, it's really all accounting details that get settled at tax time every year, and everything mixed with a large dose of mental math. What truly matters is the after-tax portion of your contribution. $10k invested that gets you $4k back means you invested $10k for the actual after-tax cost of $6k. The remaining $4k inside the RRSP actually belonged to the government, and the income tax deferral comes in the form of a matching $4k refund outside the RRSP. If you insist, you can view the refund as the $10k getting "untaxed". It will get retaxed later when you withdraw from the RRSP, for a total number of exactly one total time getting taxed.
Of course if you blow that $4k on cocaine and hookers the minute you get it, you'll end up worse off down the line than if you had invested $10k in your TFSA. But that's not due to some intrinsic property of the RRSP, it's just that $10k is more than $6k!